Title-holders Chiefs needed an extra-time goal from Zimbabwean Knowledge Musona to see off second-tier Black Leopards 1-0 in northern city Polokwane.
And Pirates had an even closer first-round call, pipping second-division Thanda Royal Zulu on penalties after a 3-3 thriller in Indian Ocean town Richards Bay.
Free State Stars were the one Premiership side beaten by lower-league opponents as they slumped 1-0 at home against Witbank Spurs.
Mamelodi Sundowns, traditional challengers to Chiefs and Pirates for league and cup crowns, won 1-0 at Ajax Cape Town 1-0 in an all-Premiership clash.
Leopards had Chiefs on the ropes at Peter Mokaba Stadium in regular time, but could not deliver the knockout blow because of poor finishing.
They were made to pay 19 minutes into extra time when a defensive slip allowed Siphiwe Tshabalala to set up substitute Musona for a close-range goal.
Once ahead, a Chiefs side lacking several rested regulars, including goalkeeper and captain Itumeleng Khune, erected an impregnable defensive barricade.
"A lot went wrong today," admitted England-born Chiefs coach Stuart Baxter. "We lost concentration in and out of possession.
"Leopards had nothing to lose and we had everything to lose. In the beginning, they had more appetite for the battle than us.
"These are difficult times with so many domestic and CAF fixtures. I pick teams and have minimal time to prepare for the match."
Chiefs hold a nine-point Premiership lead in defence of the title and host Mozambicans Liga Muculmana this Saturday in a CAF Champions League qualifier.
Leopards experienced Serb coach Kosta Papic summed up the game succinctly: "We did everything right except win the match.
"We carried no white flags - we were not afraid of Chiefs. My lone disappointment was our failure to take the scoring chances."
Former African champions Pirates trailed Thanda after just 40 seconds, were two goals behind at half-time, and netted twice in stoppage-time to force 30 additional minutes.
Substitute Kermit Erasmus nudged the 'Buccaneers' ahead in extra time only for Mhlengi Cele to equalise on 121 minutes.
The shootout proved an anti-climax with calmer Pirates winning 3-1 after converting three spot-kicks while Thanda fluffed three of four.
Rodney Ramagalela, an early substitute for injured Katlego Mashego, struck on the hour-mark for Sundowns with an unstoppable drive past Brandon Petersen.
